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We obtain similar results for the sytem\n  {equation*} \\{{array}{rrl} -\\Delta u &=& \\lambda f(v) \\qquad \\Omega, -\\Delta v &=& \\gamma g(u) \\qquad \\Omega, u&=& v = 0 \\qquad \\partial Omega. {array}. {equation*}"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1109.5206","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-09-23T22:00:54Z","cross_cats_sorted":[],"title_canon_sha256":"05bc382e2c4947766313b39293adb82d0e25b9dd751b0cac6c5e057b1cc9e3e2","abstract_canon_sha256":"0ff29e9556513b5f5f007295624cc6a8983bea142f8fcc59180b3be07c86bb4b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:12:20.383570Z","signature_b64":"HaKKa0DNl20iIy4J4qr2hvW/9lH8IrQVa5jvvHHOoYoKU+vFa8+j5XUB4bt6BskETBzOhp9mTQEKjQiyW1bMDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1043fb249a6f094cdc3de89467024a86f9428227f2bf60eb620d98ff46383647","last_reissued_at":"2026-05-18T04:12:20.382943Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:12:20.382943Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Uniqueness of solutions for elliptic systems and fourth order equations involving a parameter","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Craig Cowan","submitted_at":"2011-09-23T22:00:54Z","abstract_excerpt":"We examine the equation \\[\\Delta^2 u = \\lambda f(u) \\qquad \\Omega, \\] with either Navier or Dirichlet boundary conditions. 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